Monotonicity criterion for the interspecies correlation coefficient

Let $V^{(n)}_{a}(\alpha,0)$ and $V^{(n)}_{c}(\alpha)$ denote the anagenetic and cladogenetic contributions to the variance, and let $C^{(n)}_{a}(\alpha,0)$ and $C^{(n)}_{c}(\alpha)$ denote the corresponding contributions to the interspecies covariance. For $\alpha \ge 0$ and $n\ge 2$, Monotonicity conjecture.

$$V^{(n)}_{c}(\alpha)C^{(n)}_{a}(\alpha,0) \ge V^{(n)}_{a}(\alpha,0) C^{(n)}_{c}(\alpha).$$

This inequality is intended to be the equivalent condition for the interspecies correlation coefficient $\rho_n(\kappa)$ to decrease monotonically as $\kappa$ ranges over $(0,1)$, with it being sufficient to consider $\delta=0$. A proof is not supplied; the source notes that the relevant interactions are delicate and that only numerical plots support the expected monotone decrease.